What is (\partial)/(\partial x)(sin(3x^3y-5xy^3)) ?

The answer to (\partial)/(\partial x)(sin(3x^3y-5xy^3)) is cos(3x^3y-5xy^3)(9yx^2-5y^3)

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(\partial)/(\partial x)(sin(3x^3y-5xy^3))

\frac{\partial}{\partial x} (sin (3 x^{3} y - 5 x y^{3}))

cos (3 x^{3} y - 5 x y^{3}) (9 y x^{2} - 5 y^{3})

Solution steps

\frac{\partial}{\partial x} (sin (3 x^{3} y - 5 x y^{3}))

Treat

y

as a constant

Apply the chain rule:

cos (3 x^{3} y - 5 x y^{3}) \frac{\partial}{\partial x} (3 x^{3} y - 5 x y^{3})

= cos (3 x^{3} y - 5 x y^{3}) \frac{\partial}{\partial x} (3 x^{3} y - 5 x y^{3})

\frac{\partial}{\partial x} (3 x^{3} y - 5 x y^{3}) = 9 y x^{2} - 5 y^{3}

= cos (3 x^{3} y - 5 x y^{3}) (9 y x^{2} - 5 y^{3})

f (x) = 7 e^{x} cos (x), (0, 7)

\int cos^{7} (7 - x) sin (7 - x) d x

\int_{1}^{2} 15 x^{2} 2^{x^{3}} d x

(5 t + e^{t}) (3 - t)

(x^{2} y^{3} - \frac{1}{1 + 9 x ^{2}}) (\frac{d x}{d y}) + x^{3} y^{2} = 0

What is (\partial)/(\partial x)(sin(3x^3y-5xy^3)) ?
The answer to (\partial)/(\partial x)(sin(3x^3y-5xy^3)) is cos(3x^3y-5xy^3)(9yx^2-5y^3)